TALLAHASSEE — The legal drinking age in Florida will increase from 19 to 21 on July 1 if a bill passed Friday by the House becomes law.

The 114 to 0 vote handed Rep. Fran Carlton, D-Orlando, a hard-fought victory. She had tried for seven years to raise the drinking age but watched as opponents in unfriendly committees buried her bills.

Carlton's bill (CS/HB 54) originally called for the drinking age to increase to 20 on Sept. 30, and to 21 on Sept. 30, 1986. She agreed Friday to an amendment raising the age to 21 this year. Anyone who is 19 on or before June 30 will retain the right to buy alcohol under the amendment.

Carlton had predicted the unanimous vote Thursday. ''There's not one member of this House who wants to go home and tell constituents they didn't vote for this bill,'' she said Friday. ''It's a popular issue at home. The polls show that more than 80 percent of the public wants the drinking age raised.''

Carlton said she would spend the weekend seeking support from senators. She said liquor lobbyists will be working just as hard to persuade the Senate to undo what the House has done.

''In this arena you can't ever assume it's over until it's over. The fat lady won't sing until the last button on the Senate vote board is lit,'' she said.

She discounted the idea that many members were forced by the federal government to vote for something they oppose. The Reagan administration intends to withhold 5 percent of federal highway